**3.1 Adding family math to the equation**

To build evidence for the importance of including a family math component in a classroom mathematics intervention, we evaluated two preschool math intervention

#### *It All Adds Up: Connecting Home and School through Family Math DOI: http://dx.doi.org/10.5772/intechopen.112714*

conditions and their effects on child outcomes, relative to a practice-as-usual condition: a classroom math (CM) intervention and a classroom math plus family math (CM + FM) intervention (for more details see [57]). Using math games has been key to our approach for creating inclusive classroom and family math practices and thus, the classroom math intervention included math games and playful instructional materials, and a relatively light touch professional development (PD) course for Head Start teachers. The family math (CM + FM) intervention included the same classroom math PD and games but added family math games and resources (such as bilingual math minibooks) that teachers could send home with children. Both conditions were "ecologically valid" such that they were implemented under naturalistic conditions, implemented by the teacher with the whole class, and aimed to support more than one mathematics skill.

We conducted a clustered randomized control trial with 573 children from 66 classrooms in three Head Start programs across two states in the Northeastern United States and found that in mixed-age (3- to 5-years) Head Start classrooms, the classroom plus family math intervention was significantly associated with spring mathematics scores relative to practice as usual (effect size of *d* = .20) but the classroom math intervention (without the family math component) was not significantly associated with outcomes. This finding underscores the value of combining a familyengagement component with a classroom mathematics intervention and adds to the evidence of the key role that family engagement plays in promoting children's math learning. In addition, this finding suggests that the combined intervention (CM + FM) has potential as an effective means to fill a gap in early childhood instructional practice especially because it can be implemented at scale without substantial investments in a specific mathematics curriculum, PD, or coaching support. In fact, interventions that can be qualified as "ecologically valid" are limited, and knowing under which conditions these interventions can be considered effective is essential [81].

YM's family math component provides children with two touchpoints for the mathematics—within the classroom, and at home—thus allowing the child to become the expert who "teaches" their parent how to play the games they learned at school. Parents report that seeing their children competent and confident about math is a great source of pride. As part of our family math community partnership work, we have expanded upon these touchpoints by adding more places within the community for families and children to encounter positive experiences engaging with mathematics ideas.

Highlights from our findings showed that

